Melt the butter in a pot/microwave and set it aside.
Peel the potatoes and cut them into small cubes.
Boil them until tender, it takes anywhere from 10-20 minutes depending on the variety and season.
Add the butter and blend them (e.g., with an immersion blender) into a puree.
Then add the egg whites and milk and strain it through a fine-mesh sieve before pouring it into a siphon bottle. This recipe is based on a half-liter bottle.
Add 3 cartridges to the bottle and it's ready to serve.
If you want to ensure it maintains its temperature, you can keep it in your sous vide/water bath at 60 degrees Celsius (140 degrees Fahrenheit) - this way it can be prepared well in advance.